Assessment of Weather-Related Risk on Chestnut Productivity

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Nat. Hazards Earth Syst. Sci., 11, 2729–2739, 2011 www.nat-hazards-earth-syst-sci.net/11/2729/2011/ Natural Hazards doi:10.5194/nhess-11-2729-2011 and Earth © Author(s) 2011. CC Attribution 3.0 License. System Sciences

Assessment of weather-related risk on chestnut productivity

M. G. Pereira1,2,3, L. Caramelo1,3, C. Gouveia2,4, J. Gomes-Laranjo1, and M. Magalhaes˜ 5 1Centre for Research and Technology of Agro-Environment and Biological Sciences (CITAB), University of Tras-os-Montes´ and Alto Douro, Vila Real, Portugal 2Instituto Dom Luiz – Universidade de Lisboa, Lisboa, Portugal 3Departamento de F´ısica, Escola de Cienciaˆ e Tecnologia, Universidade de Tras-os-Montes´ e Alto Douro (DF-ECT UTAD) Vila Real, Portugal 4Escola Superior de Tecnologia, Instituto Politecnico´ de Setubal,´ Setubal,´ Portugal 5Departamento de Cienciasˆ Florestais e Arquitectura Paisagista, Escola de Cienciaˆ Agrarias´ e Veterinarias, Universidade de Tras-os-Montes´ e Alto Douro (DCFAP-ECAV UTAD) Vila Real, Portugal Received: 31 January 2011 – Revised: 20 April 2011 – Accepted: 30 May 2011 – Published: 12 October 2011

Abstract. Due to its economic and nutritional value, the 1 Introduction world production of chestnuts is increasing as new stands are being planted in various regions of the world. This work fo- According to FAO statistics (FAO, 2010), Portugal was the cuses on the relation between weather and annual chestnut sixth world’s largest producer in 2008 with 22 000 tons; the production to model the role of weather, to assess the im- world’s largest producers are China (1 000 000 tons), South pacts of climate change and to identify appropriate locations Korea (75 000 tons) Italy and Turkey (55 000 tons), and for new groves. The exploratory analysis of chestnut produc- Japan (26 000 tons), but it should be noted that all these coun- tion time series and the striking increase of production area tries have a much higher land area than Portugal (Bounous, have motivated the use for chestnut productivity. A large set 2002b). The most noteworthy facts from world chestnut pro- of meteorological variables and remote sensing indices were duction trends in the last four decades are: (i) East Asian computed and their role on chestnut productivity evaluated production continues to enlarge, mainly because of the great with composite and correlation analyses. These results al- increase in the contribution of China (from 130 000 tons low for the identification of the variables cluster with a high in the 60s of the 20th century); (ii) a general decrease in correlation and impact on chestnut production. Then, differ- the production in some western European countries (Portu- ent selection methods were used to develop multiple regres- gal, 82 000 tons in the 60s, Spain, France and Italy) and an sion models able to explain a considerable fraction of pro- increase in Turkey (40 000 in the 60s); (iii) new orchards ductivity variance: (i) a simulation model (R2-value = 87 %) have been planted in Europe, North (USA) and South Amer- based on the winter and summer temperature and on spring ica (Brazil and Chile), Australia and New Zealand, due to and summer precipitation variables; and, (ii) a model to pre- the increase of the retail price for quality nuts and pro- dict yearly chestnut productivity (R2-value of 63 %) with five cessed products and by the European Community funding months in advance, combining meteorological variables and programmes (Bounous, 2002b; Gomes-Laranjo et al., 2007). NDVI. Goodness of fit statistic, cross validation and resid- Chestnut trees are also cultivated for their fruit and wood. ual analysis demonstrate the model’s quality, usefulness and With regards to the fruit, it is used in preparations of many consistency of obtained results. recipes due to its dietetic value. Its wood is as strong as oak, but significantly lighter. In fact, results obtained by Ja- cobs et al. (2009) demonstrated that North American chestnut trees compete favourably in the aboveground allocation of biomass and carbon sequestration ability with any other species in this region. A chestnut agro-ecosystem also provides a habitat for diverse macrofungal species which sup- port a high value of economical activity such as the mush- Correspondence to: M. G. Pereira room harvesting (Baptista et al., 2010). ([email protected])

Published by Copernicus Publications on behalf of the European Geosciences Union. 2730 M. G. Pereira et al.: Assessment of weather-related risk on chestnut productivity

In Europe, the most important chestnut specie is Castanea applications in drought monitoring (Vicente-Serrano et al., sativa Mill., one of 13 species from Castanea genus. In 2006; Gouveia et al., 2009), agriculture, crop growth moni- relation to its phenology, bud break happens at the end of toring, yield modelling (Gouveia and Trigo, 2008) and crop April, the flowering period is between June and July, being identification. In particular, the time-series of satellite im- the last phase related to fruit development between August agery efficiently provide a synoptic view of vegetation dy- and October, time for fruit fall. This species, also called namics, namely the chestnut vegetative cycle that may be sweet chestnut, dislikes chalky soil, but appreciats sedimen- used for chestnut management. Phenological information tary or siliceous soils. Their roots tend to decay in poorly is, in fact, essential for decision making during many of the drained soils, which help to explain why they prosper on phases of growing, namely on management planning, pest hills and mountainsides. The European chestnut is cultivated and disease control (Gouveia et al., 2011). In this context, for its nuts and wood and can be found on acidic to neutral several vegetation indices have been used in order to describe soils, influenced by an oceanic climate which is characterised the phenology, namely the Normalized Difference Vegetation by annual mean values of sunlight spanning between 2400 Index (NDVI) as derived from remote-sensed information. and 2600 h and rainfall ranging between 600 and 1500 mm, The NDVI was designed to capture the contrast between red mean annual temperature between 9 and 13 ◦C, 27 ◦C being and near-infrared reflection of solar radiation by vegetation, the mean of the maximal temperature (Heiniger and Coned- and is an indicator of the amount of green leaf area (Asrar et era, 1992; Gomes-Laranjo et al., 2008). According to Dinis al., 1984; Myneni et al., 1995). Despite its simplicity, NDVI et al. (2011), chestnut regions must have 1900–2200 ◦D be- has been widely used in studies of vegetation phenology and tween May and October. The degree-days (◦D) is the sum of interannual variability of vegetation greenness (Gouveia et the temperature values in degrees Celsius with a base temper- al., 2008). ature of 6 ◦C (Cesaraccio et al., 2001; Dinis et al., 2011). Ac- This work aims to identify the favourable/adverse weather cordingly, in the Iberian Peninsula, this edaphoclimatic situ- conditions to chestnut production as well as helping to as- ation can be observed since sea level on seacoast regions to sess risk and to identify appropriate measures for adaptation mountainous regions (between 600 and 1000 m a.s.l.) in the to climate change. In this sense, the three specific objectives inner part of the continent. The influence of temperature and of this work are: (i) to characterise the chestnuts production radiation on photosynthesis productivity in chestnut popula- in Portugal; (ii) to quantify the role of weather and climate tions in Northeast Portugal was analysed by Gomes-Laranjo on chestnut production; and, (iii) to develop simulation and et al. (2006). Maximum photosynthetic activity occurs at prediction models of chestnut production based on meteoro- 24–28 ◦C for adult trees, but exhibits termoinhibition when logical variables and vegetation indices. the air temperature is above 32 ◦C, which is frequent during summer (Gomes-Laranjo et al., 2006, 2008). All species of plants are dependent on the weather with regards to their 2 Study area and datasets production. However, only a few number of works have been This work uses chestnut production, vegetation index and published on weather dependence of chestnut production and meteorological datasets which cover the 1982–2006 period none of references found on this subject intend to quantify and includes: and model portuguese chestnut production. Wilczynski and Podlaski (2007) concluded that the radial growth of horse – annual values of the total chestnut production and the chestnut (Aesculus hippocastanum L.) is positively related production area in Portugal, provided by the Portuguese to high air temperature of August and during the previous National Institute of Statistics (INE, 2010) (http://www. winter and negatively related to excessive precipitation in ine.pt); August. The growing season is defined as the period of – daily values of several meteorological variables reg- time when the mean 24-h temperature is greater than 5 ◦C. istered in the Bragança weather station, located at Fernandez-L´ opez´ et al. (2005) study the geographic differen- 41◦4702800 N and 6◦4504300 W, 740 m a.s.l. (Fig. 1), tiation in adaptive traits of the wild chestnut populations in namely maximum, minimum and mean temperature, Spain resorting to climate data (e.g., temperature variation, wind speed, total (rain and/or melted snow) precipi- summer precipitation/droughts and the temperature of the tation, as well as a set of weather parameters indica- warmest month) and adding evidence of the role of some me- tive of the occurrence of hail, snow, fog and storm. teorological variables, namely frost during bud break, mean This data was obtained from the Meteored web site temperature of the warmest month, summer precipitation and (METEORED, 2009); drought, creating a xerothermic index. The influence of temperature and radiation on the photosynthesis productivity in – Monthly Normalized Difference Vegetation Index chestnut populations in Northeast Portugal was analysed by (NDVI) dataset, at 8-km resolution, from the Advanced Almeida et al. (2007). Very High Resolution Radiometers (AVHRR), provided At the same time, remote-sensing technology has been by the Global Inventory Monitoring and Modelling Sys- developing steadily and its products can provide many tem (GIMMS) group (GIMMS, 2009).

Nat. Hazards Earth Syst. Sci., 11, 2729–2739, 2011 www.nat-hazards-earth-syst-sci.net/11/2729/2011/ M. G. Pereira et al.: Assessment of weather-related risk on chestnut productivity 2731

Fig. 1. 1Digital elevation model of Continental Portugal with spatial resolution of 1 km × 1 km. The colourbar represents the altitude (m). Location of Bragança weather station is identified with a black circle. 2 Figure 1. Digital elevation model of Continental Portugal with spatial resolution of Page 1/1 3 1 km × 1 km. The colorbar represents the altitude (m). Location of Bragança weather station In Portugal, chestnut orchards may be found in the NE quarter4 of theis countryidentified which with is alsoa black characterised circle. by irregular topography (Fig. 1) with Mediterranean Csb type of climate, according5 to the Koppen-Geiger climate classification (Peel et al., 2007). A description of climate, vegetation, soil specific characteristics6 and of this specific region can be found in Gomes-Laranjo7 et al. (2007, 2009). The 5th National Forestry Inventory (NFI5), provided by the Portuguese National Forestry Authority (Autoridade Flo- restal Nacional, AFN) was used to determine the exact location of chestnut orchards in Portugal (AFN, 2010). The NFI5 was based on a digital aerial-photo coverage obtained during the 2004–2006 period and on a ground survey performed from December 2005 to June 2006 allowing the defi- nition of homogeneous land parcels from the soil occupation standpoint. Based on this information, the spatial distribution of chestnut orchards (as main occupation land use) located above 500 m were produced. Then, the location and density of chestnut trees was computed based on the number of Por- tuguese Forestry Inventory (NFI5) chestnut land parcels located inside each NDVI pixels, with a size of 8 km × 8 km (Fig. 2). The high density of chestnut trees is located in the ad- ministrative districts of Bragança and Vila Real, which con- Fig. 2. Location of the pixels (8 km × 8 km) with chestnut trees stitutes the Tras-os-Montes´ and Alto Douro region, in an as the main occupation with an altitude above 500 m. The colour area of low mountains (Marao,˜ Montezinho) and narrow bar represents the number of land parcels with chestnut trees as the valleys, in particular, in a sub-region characterised by low main occupation, identified by the 5th National Forestry Inventory, air temperature during the winter named Terra-Fria (Cold NFI5 (AFN, 2010), inside a GIMMS pixel (GIMMS,25 2009); only Land) (Fig. 1, right panel). Approximately 85 % (25 644 ha) the pixels with more than 10 chestnut trees were selected. of the 30 097 ha of the Portuguese chestnut tree area in 2006 was located in this region, which motivates the use of www.nat-hazards-earth-syst-sci.net/11/2729/2011/ Nat. Hazards Earth Syst. Sci., 11, 2729–2739, 2011

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2732 M. G. Pereira et al.: Assessment of weather-related risk on chestnut productivity meteorological data registered in Terra Fria. In addition, pre- 3 Method vious studies about chestnut weather-dependence were performed on chestnut orchards in the Tras-os-Montes´ region After a preliminary quality and exploratory analysis of the (Pires et al., 1995; Martins et al., 2005; Raimundo, 2003; raw data, composite and correlation analysis were used to Raimundo et al., 2001, 2004, 2009; Fonseca et al., 2004; identify the meteorological variables and parameters with Gomes-Laranjo et al., 2005, 2006, 2008). For these reasons, the potential to influence chestnut production/productivity we decide to use the data from the Bragança weather station in Portugal. Composite analysis is used to recognize the which is included in the meteorological observation national meteorological variables that present significant differences network, is well-situated in this region and can characterise between years of extreme positive and extreme negative weather local features. chestnut production/productivity. Composite analysis is Preliminary analysis on the meteorological dataset for based on the arithmetic mean of the meteorological vari- Bragança weather station reveals only a small fraction of sus- ables/parameters for selected yearly values of chestnut pro- picious (extremely low) or missing values for temperature duction/productivity and, eventually, it is followed by an (0.45 %). Missing values for wind speed, precipitation also anomaly analysis (defined as the difference between the com- accounts for a minute fraction of the total number of records posite and the arithmetic mean evaluated using all records) (0.16, 0.21 and 0.47 %, respectively). Monthly means and or by the assessment of the relative difference (RD) be- + medians were evaluated taking into account the missing val- tween composites obtained for extreme positive (C ) and ex- − + − − ues. However, weather parameters, indicative of the occur- treme negative years (C ), defined as RD = (C −C )/C . rence of hail, snow, fog and storm, should be used carefully Composite analysis is widely and lengthily used in atmo- since they have a much larger amount of missing values and spheric sciences and climatic research (Jury and Pathack, present some inconsistencies with meteorological variables. 1991; Bauer and Del Genio, 2006; Pereira et al., 2005; Trigo Based on the evidence found in the literature about et al., 2006). the meteorological influence on the chestnut produc- The extreme positive/negative years were defined as the tion/productivity (Bounous, 2002a; Fernandez-Lopez´ et al., years for which production or productivity time series are 2005; Wilczynski and Podlaski, 2007; Gomes-Laranjo et greater/smaller or equal to the time series arithmetic mean al., 2006, 2008), we compute a large set of meteorologi- value plus/minus the standard deviation. Using this criterion, cal variables (e.g., maximum, minimum and mean tempera- the years of 1989, 1990, 2000 and 2003 were classified as ex- ture and precipitation averages for specific group of months) treme positive while the years of 1991, 1992 1993 and 2005 and meteorological parameters, such as monthly number were classified as those that present extreme negative pro- of days with maximum, minimum and mean temperature ductivity. The criterion used to identify the extreme years is above/below/between defined thresholds (e.g., number of shown to be very suitable as it allows the classification of the days with minimum air temperature below 0 ◦C in January, same number of positive and negative extreme years that are ◦ NDays (TMin(1) < 0 C), number of days in August with max- relatively well spanned within the study period. Other cri- ◦ ◦ imum air temperature above 32 C, NDays(TMax(8) > 32 C) teria (e.g., production or productivity above/below previous or the number of days with maximum temperature between time series value plus/minus 10 %) were tested, but no signif- ◦ ◦ ◦ ◦ 24 C and 28 C in June, NDays (24 C < TMax (6) < 32 C) icant changes were found when the same number of extreme and monthly number of days with hail, snow, fog and storm. years had to be considered. The numbers in parenthesis (separated by comas) represents The correlation analysis objective is to measure the the month when the data used to compute the variable was strength of the linear relationship between chestnut produc- obtained. tion/productivity and meteorological variables/parameters The monthly NDVI dataset covers the area between 10◦ W through the evaluation of the Spearman correlation coeffi- to 0◦ E and 35◦ to 45◦ N, and respect to the 25-yr long pe- cient. This complementary technique was applied for differ- riod from 1982 to 2006. Details on the quality of GIMMS ent subperiods (e.g., 1982–1990, 1991–1999, 1999–2006), dataset may be found in Kaufmann et al. (2000) and Zhou for moving subperiods with a constant length (e.g., 5, 10 and et al. (2001). We have used the information about vegeta- 15 yr) within the period of analysis, for periods with increas- tion density from NFI5 in order to select the NDVI pixels in ing and decreasing length, onward and backward, starting this region and corresponding to chestnut orchards (as main from the first and last years. occupation land use) located above 500 m. (Fig. 2). The After the identification of the potential meteorological colour bar in Fig. 2 represents the number of land parcels predictors, we use SAS software (Statistical Analysis Sys- with chestnut trees as the main occupant, identified by NFI5, tem, v9.1.3) to develop a multiple linear regression model inside a GIMMS-NDVI pixel; only the pixels with more to simulate and to predict chestnut production/productivity than 10 chestnut trees were selected. Monthly composites of with different selection methods (e.g., stepwise, forward and NDVI and corresponding anomalies for the considered pe- backward). A comprehensive description of these predictor riod were accordingly computed for the period and pixels selection methods can be found in Austin and Tu (2004), considered. Miller (1984, 2002) and Hocking (1976). In this context,

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Fernandez-Lopez´ et al. (2005) have used a linear regression cross-validation techniques, i.e., to split the available time analysis between Spanish chestnut population performance, series into calibration and validation periods. The evaluation climatic and geographic data. of model performance and the prevention of overfitting was Among other assumptions, linear regression requires that done by means of leave-one-out cross-validation technique, predictors are linearly independent (collinearity), samples i.e., by using a single observation from the original sample are representative of the population and that the error terms as the validation data and the remaining observations as the have zero mean, constant variance (homoscedasticity), nor- training data. mality (for hypothesis testing purposes) and be uncorrelated. Shapiro-Wilk test, Kolmogorov-Smirnov test as well as Lillefors test (which is an adaptation of the Kolmogorov- 4 Results Smirnov test) will be used to test if the null hypothesis that Apparently, the location of orchards are determined by soil data come from a normally distributed population. On the and climate conditions. In continental Portugal, 86 % of the other hand, predictors and predictant frequently present a total number of pixels, with chestnut trees as the main soil natural sequence (e.g., weather parameters), which means occupant, is located between 500 and 1000 m in altitude, that the errors in time series data exhibit serial correlation, where the chestnut trees may have found suitable conditions i.e., are autocorrelated. The Durbin-Watson statistic (d) is for their development, which helps to explain the strong re- used to test the presence of autocorrelation and can assume semblance between the location of chestnut orchards (Fig. 2) values between 0 and 4. When d = 2 is indicative of no au- and the Portuguese elevation map (Fig. 1). The great ma- tocorrelation while, when d < 2 there is evidence of positive jority of the chestnut production comes from areas of higher serial correlation, which means that succeeding error terms altitude namely the Terra Fria included in the Tras-os-Montes´ are, on average, similar to one another. On the other hand, and Alto Douro region, where the landscape is dominated by when d > 2 the following error terms are, typically, much the low slopes of the plateau Transmontano. High density different to one another, i.e., negatively correlated which can of chestnut trees in Portugal and in Spain are found in the imply an underestimation of the level of statistical signifi- same geographical region, extending from NE Portugal and cance. Galicia to Navarra, through coastal NW Spain (Fernandez- To assess the goodness-of-fit, residual analysis was per- Lopez´ et al., 2005). The exceptional increase in the produc- formed and several statistics were evaluated. Since the objec- tion area time series between 1991 and 1999 (Fig. 3) has a tive of this work is to study the influence of weather on chest- profound impact on the chestnut production time series vari- nut productivity, it is important to consider the coefficient of ability reflected in the increase of the average chestnut pro- multiple determination (R2) which accounts how successful duction from 18 000 ton during the first third of the period to the fit is in explaining the variation of the data, that is, how 30 000 ton in the last third, which has been related to Euro- much chestnut productivity time series variance is explained pean Community funding programmes (EEC Regulation N◦ by the developed regression model. Adding predictors to the 2080/92). This fact does not allow a proper comparison be- model, in general, increases the R2 value, but not necessarily tween chestnut production values in different periods which the usefulness of the model, in the sense of the prediction of induce the use of chestnut productivity instead of chestnut future outcomes. To take into account eventual over fitting, production in our analysis. R2 should be adjusted (R2 ) taking into account the residual Adj In general, it is assumed that the trend in the chestnut pro- degrees of freedom, which can be used for proper compari- ductivity time series can be due to factors that do not remain son between models with different numbers of independent constant during the study period such as the introduction of variables. new agriculture techniques, pesticides, laws and government In addition, other usual statistics were also determined, policies, crop diseases and plagues (Portela et al., 1999; Gen- namely: the sum square error (SSE), the mean square er- tile et al., 2009; Ghezi et al., 2010). In fact, chestnut diseases, ror (MSE) or root mean square error, and Mallows’ CP. The such as ink and cancer, which reached Portugal in the 19th RMSE is just the square root of MSE which is defined as century and ended in the 20th century, respectively, could be the quotient between SSE and residual degrees of freedom. among the possible reasons for the long-term linear decreas- Values of RMSE, MSE and SSE closer to 0 are indicative ing tendency (Kiple and Ornelas, 2000). Removing these of better models (useful for prediction). Mallows’ CP, (Mal- trends, we are expecting that variability of the detrended lows, 1973) can be used as a predictor selection criterion and chestnut productivity is only due to climate variability, since to assess the model fit, in particular, with respect to over fit- changes in climate or soil are expected to have impacts on ting since the estimates of the mean squared prediction error much longer time scales. A similar procedure was followed does not necessarily decrease as more variables are included to correct the chestnut tree-ring chronology which shows a in the model like other error measures (e.g., SSE). constant decreasing trend as trees became older (Wilczynski Statistical models, developed with relatively short time se- and Podlaski, 2007). ries, are particularly prone to overfitting problems (Wilks, 1995), to solve this caveat it is advisable to apply www.nat-hazards-earth-syst-sci.net/11/2729/2011/ Nat. Hazards Earth Syst. Sci., 11, 2729–2739, 2011 2734 M. G. Pereira et al.: Assessment of weather-related risk on chestnut productivity

a) 35 35

30 30 ton) 3 ha) 3 25 25 10 × 10 ( × ( 20 20

15 15

10 10 Production area Chestnut production Production area Production 5 5 1 Chestnut production Chestnut 0 0 2 FigureFig. 4. AnnualAnnual cycle cycle of of monthly monthly NDVI NDVI values values for for the the standard standard hydrological hy- year spanning 1980 1985 1990 1995 2000 2005 2010 3 fromdrological September year of spanningyear n-1 to from August September of year n of (wit yearh nn from− 1 to1982 August to 2006). The bottom/top Year of year n (with n from 1982 to 2006). The bottom/top indicates 1 4 indicates the lower/upper quartiles, and the band near the middle of the box is the median. b) the lower/upper quartiles, and the band near the middle of the box 1.60 5 The lower/upper end of the whiskers represents the lowest/highest observed value still within CP = -13.5 ×10 -3×Year + 28.1 is the median. The lower/upper end of the whiskers represents the 1.40 R² = 34% 6 1.5lowest/highest of the interquartile observed range valueof the lower/upper still within q 1.5uartile. of the interquartile

) range of the lower/upper quartile. -1 1.20 7 1.00 (ton.ha 0.80 signiﬁcant at 97.73 % level), when the production area al-

0.60 most doubled its value, from 15 000 ha to 29 000 ha (Fig. 3a). To circumvent this difficulty, we decide to analyse the chest- 0.40 Productivity Chestnut productivity Chestnut productivity detreend nut productivity instead of the chestnut production. Chest- 0.20 nut productivity is defined as the ratio between yearly chest- 0.00 nut production and correspondent yearly production area 1980 1985 1990 1995 2000 2005 2010 (Fig. 3b). Year 2 The productivity time series presents a linear negative − × −3 −1 −1 3 Figure 3. Observed values of: a) chestnut production, (in ×10 3 ton) and production area (in trend of 13.5 10 ton ha yr (statistically significant Fig. 3. Observed values of: (a) chestnut production, (in ×103 ton) 4 ×10 3 ha); and, b) chestnut productivity and detrended chestnut productivity (in ton.ha -1), in at 99.50 % level) which corresponds to an approximate de- and production area (in ×103 ha); and, (b) chestnut productivity and −1 5 Portugal. Colocar (a) e (b) nas figuras superior e inferior, respectivamente. crease of 300 ton yr , if the arithmetic mean value of the detrended chestnut productivity (in ton ha−1), in Portugal. 6 production area of 22 000 ha is considered. On the other

27 hand, it is expected that the detrended time series variability is only due to factors that presents constant variabil- The obtained productivity time series (Fig. 3) present ity during the study period, such as meteorological vari- an outlier in the year of 1993 for two main reasons: un- ables/parameters and soil characteristics (Cantelaube et al., favourable climate conditions and inertial delay in the ef- 2004; Gouveia and Trigo, 2008). For these reasons, we de- fect of production area increasing. In fact, in this year, the cided on the detrended chestnut productivity and, hereafter, mean air temperature during summer (June, July, August and all the following results are referred to the Corrected Produc- ◦ September) was 2.7 C below the average. In addition, chest- tivity (CP) time series (Fig. 3b). nut production in 1993 seems to follow the decreasing trend The annual cycle of NDVI monthly mean values is rep- registered in the previous period since the effect of the in- resented in Fig. 4 by means of boxplots and can be used to 28 crease of the production area is not yet felt because it is illustrate the intra-annual variability of chestnut productivity. unlikely that the recently planted chestnut trees are at their In this case, we have adopted the standard hydrological year, maximum production capacity. spanning from September of year n-1 to August of year n (with n from 1982 to 2006). The bottom/top indicates the 4.1 Chestnut production characteristics and potential lower/upper quartiles, and the band near the middle of the predictors box is the median. The lower/upper end of the whiskers represents the lowest/highest observed value still within 1.5 of The chestnut production area in Portugal is not constant dur- the interquartile range of the lower/upper quartile. It may be ing the study period. In the 1982–1990 and 1999–2006 sub- noted that winter shows a higher variability than in summer, periods, the production area time series presents a small in- presenting February and May with the most concentrated dis- creasing trend of 195 ha yr−1 (R2 = 97 %) and 215 ha yr−1 tribution. The NDVI cycle presents the maximum in early (R2 = 94 %), respectively, without statistical signiﬁcance. summer (June) and the minimum during winter (December), However, it is evident an abrupt positive trend between a feature that is related to the vegetative cycle of chestnut. 1991 and 1999 of 1.5 × 103 ha yr−1,(R2 = 99 %, statistical

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Based on preliminary results obtained in the composite time series (CPsim), is obtained with six meteorological pre- and correlation analysis, additional meteorological param- dictors selected as follows, eters were computed to obtain additional parameters that = × ◦ present higher correlation coefficient with the CP time series CPsim 0.012 NDays TMax(9) < 28 C ◦ for the reason that the SAS software tends to select the vari- −0.007×NDays TMin(2) < 10 C + ables/parameters which present high correlation with CP. For +0.06×TMax(1,9) example, accumulated precipitation in April, P (4) and July, +0.035×TMax(7) P (7) were merged into the accumulated precipitation in those + × + × − two months, P (4,7) aiming to have a variable with higher 0.002 P(4,7) 0.001 P(9) 2.268 (1) correlation coefficient with CP than P (4) or P (7). Failing to ◦ where NDays (TMax(9) < 28 C) represent the number of days present all results from the composite and correlation anal- in September with maximum air temperature below 28 ◦C (# ysis, we decided to present only those for a set of selected ◦ of days), NDays (TMin(2) < 10 C) represent the number of variables (Table 1). February days with minimum air temperature below 10 ◦C Composite analysis reveals that, in general, higher val- (# of days), TMax(1,9) is the mean maximum air tempera- ◦ ues of the relative difference between composites obtained ture in the months of January and September ( C), TMax(7) for extreme positive and extreme negative years were ob- is the mean maximum air temperature in the month of July tained for precipitation, minimum temperature and param- (◦C), P (4,7) and P (9) accounts for the accumulated precip- eters based on the number of days respecting some cri- itation (mm) in the months of April and July, and Septem- teria, than for NDVI, mean or maximum air temperature. ber, respectively. This model is obtained with both forward This finding is consistent with the nature of these vari- and stepwise selection methods and all variables included are ables in the sense that variables of the former set have statistical significant at 0.05 level. Observed and simulated a more irregular behaviour and, even the same absolute CP obtained with the more robust approach from the leave- changes produce lower relative changes in the latter set. one-out cross validation are shown in Fig. 5, while values of Some of the most significant results obtained from composite goodness-of-fit measures are presented in Table 2. The re- ◦ analysis were found for NDays (TMin(2) < 10 C), TMin(1,2), sults of the composite and correlation analysis for these pre- ◦ ◦ NDays(24 C < TMax(3) < 28 C), P (12), P (4) and P (7) with dictors are shown in Table 1. The good agreement between RD of −179 %, 123 %, 100 %, 69 %, 67 % and 60 %, respec- the modelled time series by the regression model and the one tively. obtained by the cross-validation (R = 0.99) is an indication of Results of the correlation analysis does not exactly the robustness of the developed model. This is further sup- match those from composite analysis, in the sense that ported by the relatively slight decrease (from 0.93 to 0.88) variables/parameters with the highest RD do not present of the correlation between the original and the two modelled the highest correlation coefficient with CP. In most cases, time series (by simple regression and by cross-validation). it is possible to obtain higher values of the correla- With the objective to develop a chestnut productivity tion coefficient for variables using data from two or model with prediction capability, we repeat the process but more months than for monthly variables/parameters. This restricting the meteorological variables/parameters predic- fact motivated the use of data from several months to tors to those that use basic information before the month of get better correlated variables with CP. In fact, mete- June, which means, at least, five months before the collecting orological variables/parameters which present high cor- period. Regression analysis, results in a model to predict the relation coefficient for the 1982–2006 analysis period detrended chestnut productivity time series (CPpred) with an ◦ are: TMax(1,9), TMax(1,2,9), NDays(TMax(11) < 28 C), R2-value of 63 %, based on four predictors as follows, ◦ ◦ NDays(24 C < TMax(5,6,7) < 28 C), P (4,7) and TMean(2,9) with ρ equals to 63 %, 60 %, 56 %, 49 %, 48 % and 48 %, re- CPpred = 0.019×TMean(1,2,3) spectively. The same type of variable/parameters, e.g., accu- +0.002×P(4)−0.002×P(5) mulated precipitation, could present positive correlation co- +0.001×NDVI500(5)+0.146 (2) efficient for one period of the year and negative correlation for another, reflecting the role of precipitation in the different where, TMean(1,2,3) is the mean air temperature in the ◦ moments of the vegetative cycle. months of January, February and March ( C), P (4) and P (5) are the precipitation registered in the months of April and 4.2 Chestnut productivity simulation and prediction May (mm), respectively, and, finally, NDVI500(5) accounts models for the NDVI for the pixels with chestnut trees as the main occupant located above 500 m in May. Observed (CPobs) and All the meteorological variables/parameters produced were simulated (CPpred) chestnut productivity with the leave-one- tested with the predictor selection/elimination methods in the out cross-validation model is shown in Fig. 5, while model regression analysis and the best simulation regression model robustness measures are presented in Table 2. Results of the (R2-value = 87 %) of the detrended chestnut productivity composite and correlation analysis for these predictors are www.nat-hazards-earth-syst-sci.net/11/2729/2011/ Nat. Hazards Earth Syst. Sci., 11, 2729–2739, 2011 2736 M. G. Pereira et al.: Assessment of weather-related risk on chestnut productivity

Table 1. Values of: (i) the relative difference between composites obtained for positive and negative years; and, (ii) the Spearman correlation coefﬁcients between selected meteorological parameters and corrected chestnut productivity. TMean, TMax and TMin are the average of the mean, maximum and minimum air temperature; P is the accumulated precipitation, NDays accounts for the number of days that meets the condition in brackets and NDVI500 represents the NDVI for the pixels with the chestnut trees as the main occupant located above 500 m. All variables/parameters were computed for a speciﬁc month or group of months indicated in parenthesis.

Composite Correlation Meteorological analysis analysis parameters RD = (C+ −C−)/C− (%) 1982–2006

TMean(1,2,3) 21.4 30 TMax(1,9) 8.7 63 TMax(7) −0.3 7 P (4,7) 66.3 48 P (4) 66.7 46 P (5) −29.2 −30 P (9) −18.2 1 ◦ NDays (TMin(2) < 10 C) −179 −26 ◦ NDays (TMax(9) < 28 C) 0.0 −10 NDVI500 (5) 6.9 30 NDVI500 (1) 2.5 27

2 2 2 Table 2. Values of the goodness-of-ﬁt statistics (coefﬁcient of multiple determination, –R –, adjusted R ,–RAdj–, Mallows’ CP, Durbin Watson, d, sum square error, SSE, and the mean square error, MSE) for simulation and prediction chestnut productivity multiple regression models.

2 2 Goodness-of-ﬁt statistics R Radj CP d MSE SSE Simulation Model 0.8651 0.8201 7.0000 2.272 0.0035 0.0633 Prediction Model 0.5755 0.4907 5.0000 2.034 0.0100 0.1993

presented in Table 1. For this model, cross-validation results Results for simulation model dL0.05 < (4−d) < dU0.05 re- are slightly lower, but what is still noticeable is the great re- veal that there is no statistical evidence that the error terms semblance between both modelled time series (R = 0.97) and are negatively nor positively correlated while for prediction the small reduction (from 0.79 to 0.65) of the correlation be- model (4−d) > dU0.05 there is statistical evidence that the tween the observed and the two modelled time series. error terms are not negatively autocorrelated. Linear regression assumptions were not violated given that: complete chestnut productivity time series was used 5 Discussion and conclusions in this work; exploratory analysis of the residuals reveals that residuals of both models have zero mean and con- Composite and correlation analysis allows the identification stant variance; all normality tests performed (Shapiro-Wilk, of the meteorological variables/parameters with the highest Kolmogorov-Smirnov and Lilliefors) confirm that the null potential to have impacts on the chestnut productivity. Actu- hypothesis that residuals of both models have a normal distri- ally, variables with the highest RD and correlation coefficient bution cannot be rejected. In addition, values of the Durbin- with CP, were selected by the selection methods during the Watson statistic (d) for both models are not very different regression analysis. However, it is clear that not only vari- from the value (d = 2) of uncorrelated error terms but, while ables with high RD and, simultaneously, highly correlated for simulation model it could be indicative of negative au- with CP were selected as predictors of simulation and pre- tocorrelation (d = 2.272), for prediction model (d = 1.855) it diction models. could be a sign of positive autocorrelation. A test for posi- The regression analysis results obtained are dependent on tive and negative autocorrelation (which are not frequent), at the size of the pool of potential predictors used in the anal- significance α, is based on the comparison of statistic (4−d) ysis, as well as on the selection method adopted. In fact, with lower and upper critical values (dL, α and dU, α), de- the use of a backward elimination method on a sufficient pending on the sample size and the number of regressors. large pool of predictors, allows us to obtain a perfect model

Nat. Hazards Earth Syst. Sci., 11, 2729–2739, 2011 www.nat-hazards-earth-syst-sci.net/11/2729/2011/ M. G. Pereira et al.: Assessment of weather-related risk on chestnut productivity 2737

1.6 abnormal high temperatures in September, which allows the )

-1 Observed Simulated CV Predicted CV growth of the nuts and avoids the thermo inhibition of the 1.4 trees (Gomes-Laranjo et al., 2005, 2006). The use of sev- 1.2 eral precipitation predictors (P (4), P (5), P (4,7) and P (9)) (ton.ha 1.0 in both simulation and prediction models reflects the importance of rainfall for chestnut productivity. The relative 0.8 abundance of precipitation in April and May provides the 0.6 2 2 RSim = 77% RPred = 42% appropriate soil humidity conditions that favours budbreak. 0.4 On the other hand, the occurrence of precipitation in July and September, during the chestnut development, also re- 0.2 flects the existence of mild temperature during the summer Chestnut productivity Chestnutproductivity 0.0 and, since precipitation in these months are usually of small 1982 1986 1990 1994 1998 2002 2006 amounts, does not compromise the flushing. In fact, summer Year 1 drought/precipitation was also identified as an important fac- 2 Figure 5. Values of observed (dashed with diamonds) and modelled with cross validation tor in the relation between flushing and its coefficient of vari- Fig. 5. Values of observed (dashed with solid diamonds) and mod- 3 (CV) with simulation (solid with grey circles) and prediction (solid light grey with white ation in Spanish chestnut orchards (Fernandez-Lopez´ et al., elled with cross-validation (CV) with simulation (solid with grey 4 diamonds) model of detrended chestnut productivity in Portugal, for the 25-year period, circles) and prediction (solid light grey with white diamonds) model 2005). Finally, NDVI500(5) reflects the physiological state 5 defined from 1982 to 2006. R2 -values between observed and modeled time series with CV of detrended chestnut productivity in Portugal, for the 25-yr period, of chestnut trees in the end of Spring, that results from the 6 are also shown. defined from 1982 to 2006. R2-values between observed and mod- combined effect of mild temperature and the relative abun- 7 elled time series with CV are also shown. dance of precipitation during the previous winter and early 8 spring.

9 Near zero value of the sum of squared error and of the (R2-value of 100 %) for both the simulation and prediction mean squared error reveals that simulation and prediction 10 of CP. However, these models make use of a large number model have small random error component and that are use- 11 of predictors which is not acceptable from the statistical or ful for prediction. The small decrease of the adjusted R2 12 physical point of view. In order to obtain more realistic mod- in relation to R2 for simulation (4.5 %) and prediction model els, instead of reducing the number of potential predictors (8.5 %) as well as the continuously decreasing values of Mal- with any ad-hoc criterion, we decide to restrict the solutions low’s CP during predictor’s selection process suggest that provided by the forward and stepwise selection methods. both models should not be especially affected by over fitting. It should be underlined that all the predictors retained in For models not suffering from appreciable lack of fit (bias), the models by both selection methods are statistically signif- the CP values should be similar to the number of predictors, icant at the 0.0500 level and do not employ the same basic in-29 which is the case for both models. Better results obtained for formation (for example, variables such as TMean(7,8,9), i.e., a simulation model are unsurprisingly due to the use of ad- the mean air temperature in July, August and September and ditional and more pertinent predictors which is reflected by 2 TMean(7), i.e., the mean temperature in July, were not used higher values of R . simultaneously in the model. In addition, the presented mod- In summary, the main conclusions from this work are: els are parsimonious and useful, in the sense that it does not (i) time series of chestnut production, and production area include a large number of predictors and present the highest present statistical characteristics that led to the use of produc- R2-value which means that these models explains the highest tivity time series; (ii) the use of composite and correlation percentage of chestnut productivity inter-annual variability, analysis allows the identification of the meteorological pa- with the predictors tested. rameters with high impact on chestnut productivity, in good Furthermore, it is possible to find a phenological inter- agreement with previous results; (iii) regression analysis en- pretation for each predictor used in the models. In fact, it ables the selection of the predictors to be used in simulation should be expected that high productivity is associated with and prediction models; (iv) all the predictors retained are sta- a warm and relatively long growing season and a mild win- tistically significant at 0.05 level and obtained models are ter (Wilczynski and Podlaski, 2007), which is explained by simple and parsimonious (linear and with few parameters); the positive values of the estimated parameters for TMax(1,9), (v) productivity time series is well reproduced by simulations TMax(7), TMean(1,2,3) and the negative value estimated for which means that weather (during all the vegetative cycles ◦ the parameter of NDays(TMin(2) < 10 C). This result is also of the chestnut trees) explains a relatively high percentage associated with the fact that high chestnut production re- of original time series variance; (vi) all regression verifica- quires, at least, 6 months with mean air temperature above tion procedures (goodness-of-fit, residual analysis and cross- 10 ◦C (Gomes-Laranjo et al., 2008). On the other hand, validation results confirms the quality, usefulness and robust- ◦ NDays(TMax(9) < 28 C) predictor evaluation was based on ness of the models. the temperature range where chestnut trees have a maxi- The establishment of the relation between weather and mum photosynthetic activity and reflects the inexistence of chestnut productivity is not a simple task due to several

www.nat-hazards-earth-syst-sci.net/11/2729/2011/ Nat. Hazards Earth Syst. Sci., 11, 2729–2739, 2011 2738 M. G. Pereira et al.: Assessment of weather-related risk on chestnut productivity factors. Production depends on the production area, but also Asrar, G., Fuchs, M., Kanemasu, E. T., and Hatfeld, J. L.: Estimat- on many other factors that were not taken into account in ing absorbed photosynthetic radiation and leaf area index from the work such as chestnut variety (Gomes-Laranjo et al., spectral reflectance in wheat, Agron. J., 76, 300–306, 1984. 2006), tree age, altitude of the orchards and solar exposition Austin, P. C. and Tu, J. V.: Automated variable selection methods (Almeida et al., 2007), government policies, soil degradation for logistic regression produced unstable models for predicting (Portela et al., 1999, Raimundo 2009), chestnut tree diseases acute myocardial infarction mortality, J. Clin. 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